Summary A fundamental problem of neuroscience is understanding the operation of cerebral cortical circuits. Given the basic similarity of all cortical circuitry despite many differences across species and areas, understand- ing of any particular cortical circuit will be a major step toward that goal. Here we propose to bring an extremely strong team of theorists together to model the circuitry of mouse primary visual cortex (V1) in unparalleled depth, in tight interaction with experimentalists who will produce transformative data to inform and test our models. We will initially focus on understanding contextual modulation and its modulation by running and arousal in layer 2/3 processing, incorporating the three best-studied subtypes of inhibitory neurons, parvalbumin- (PV), somatostatin- (SOM), or vasoactive-intestinal-peptide-expressing (VIP) interneurons, and possible subtypes of SOM neurons. We will also develop tractable single-compartment models of dendritic inhibition, which will be a critical advance allowing network models to address the function of different interneuron types targeting different neuronal compartments while remaining simple enough to yield insight. We will study the impacts on network behavior of SOM inhibition at dendrites vs. PV inhibition on soma and of the short-term plasticity of synapses in the system. We will then advance to incorporating further subtypes, addressing a wider range of dynamic response properties, and modeling layer 4 and the full system of layers 2 through 4, building on the extensive data gathered by experimental projects in this proposal. Finally, working with Project 1, we will develop a uni?ed model of mean stimulus responses and correlated ?uctuations, and address V1 responses to natural stimuli. To understand the functions of cortical specializations such as cell subtypes and layers, we must not only systematically incorporate structure revealed in the data, but use modeling approaches aimed at gaining insight, e.g. understanding mechanisms that produce speci?c activities, or the forms of circuit modulation that can result from targeting particular cell types in particular combinations. To achieve this, we will gradually, step-by-step, add complexity to our models, understanding at each step what new behaviors are introduced, what greater structure or alterations occur in previously understood mechanisms, and what new mechanisms become visible. The most innovative aspect of this proposal is that we will use theoretical approaches designed to give in- sight into mechanisms to grapple with the complex speci?c details of mouse V1. Existing approaches typically either study more abstract models (e.g., generic excitatory and inhibitory cells) or put all known details (along with, necessarily, a great many unknown ones) into the computer with the belief that this will reproduce brain activity, an approach unlikely to generate functional responses or testable predictions. Our approach promises to dramatically deepen our insight into the mechanisms of processing in cortex and in mouse V1 in particular.